Question: Simplify the following expression: $k = \dfrac{15np - 25mp}{15p^2 - 5p} + \dfrac{20mp + 10p^2}{15p^2 - 5p}$ You can assume $m,n,p \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{15np - 25mp + 20mp + 10p^2}{15p^2 - 5p}$ $k = \dfrac{15np - 5mp + 10p^2}{15p^2 - 5p}$ The numerator and denominator have a common factor of $5p$, so we can simplify $k = \dfrac{3n - m + 2p}{3p - 1}$